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This approach uses a Union-Find (Disjoint Set Union, DSU) structure to detect cycles and check for nodes with two parents. The goal is to handle two situations: a node having two parents, and a cycle existing in the graph. We iterate through the edges to identify a node with two parents and mark the offending edge. Then, we use the Union-Find structure to track cycles and find the redundant connection based on the identified edges.
Time Complexity: O(n), where n is the number of edges.
Space Complexity: O(n), for storing the parent and rank arrays.
1#include <stdio.h>
2#include <stdlib.h>
3
4typedef struct UnionFind {
5 int* parent;
6 int* rank;
7} UnionFind;
8
9UnionFind* createUnionFind(int size) {
10 UnionFind* uf = (UnionFind*)malloc(sizeof(UnionFind));
11 uf->parent = (int*)malloc(sizeof(int) * size);
12 uf->rank = (int*)malloc(sizeof(int) * size);
13 for (int i = 0; i < size; i++) {
14 uf->parent[i] = i;
15 uf->rank[i] = 1;
16 }
17 return uf;
18}
19
20int find(UnionFind* uf, int x) {
21 if (uf->parent[x] != x) {
22 uf->parent[x] = find(uf, uf->parent[x]);
23 }
24 return uf->parent[x];
25}
26
27void unionSets(UnionFind* uf, int x, int y) {
28 int rootX = find(uf, x);
29 int rootY = find(uf, y);
30 if (rootX != rootY) {
31 if (uf->rank[rootX] > uf->rank[rootY]) {
32 uf->parent[rootY] = rootX;
33 } else if (uf->rank[rootX] < uf->rank[rootY]) {
34 uf->parent[rootX] = rootY;
35 } else {
36 uf->parent[rootY] = rootX;
37 uf->rank[rootX]++;
38 }
39 }
40}
41
42int* findRedundantDirectedConnection(int** edges, int edgesSize, int* edgesColSize, int* returnSize) {
43 int n = edgesSize;
44 int* parent = (int*)malloc(sizeof(int) * (n + 1));
45 for (int i = 0; i <= n; i++) {
46 parent[i] = i;
47 }
48 int* can1 = NULL;
49 int* can2 = NULL;
50 for (int i = 0; i < n; i++) {
51 int u = edges[i][0], v = edges[i][1];
52 if (parent[v] != v) {
53 can1 = (int*)malloc(sizeof(int) * 2);
54 can2 = (int*)malloc(sizeof(int) * 2);
55 can1[0] = parent[v];
56 can1[1] = v;
57 can2[0] = u;
58 can2[1] = v;
59 edges[i][1] = 0;
60 } else {
61 parent[v] = u;
62 }
63 }
64
65 UnionFind* uf = createUnionFind(n + 1);
66 for (int i = 0; i < n; i++) {
67 if (edges[i][1] == 0) continue;
68 int u = edges[i][0], v = edges[i][1];
69 if (find(uf, u) == find(uf, v)) {
70 if (can1) return can1;
71 int* result = (int*)malloc(sizeof(int) * 2);
72 result[0] = u;
73 result[1] = v;
74 return result;
75 }
76 unionSets(uf, u, v);
77 }
78 return can2;
79}
80The implementation uses a Union-Find data structure to manage connectivity among nodes and track potential redundant connections by checking parent-child relationships and detecting cycles. First, it checks whether any node has two parents. If found, it temporarily removes that edge and continues to apply Union-Find to check for any cycles. If a cycle exists without finding a node with two parents, the wrong edge is part of the cycle. Otherwise, it'll be the edge removed previously.
In this method, we focus on identifying two scenarios: an edge creating a cycle in the graph and a node with two parents. With graph traversal, primarily cross-check with parent pointers and DFS for cycle confirmation, fine-tuning insights to pinpoint a last array occurrence redundant connection.
Time Complexity: O(n^2) with recursive verification.
Space Complexity: O(n), memoizing visited nodes.
1#
Utilizing DFS, this C code ensures settings target node connections and traces for potential overlapping cycles, using indications to determine redundancy. Understanding traversal in view of directed graph properties is fundamental to isolating missteps.